Kernel-based Fisher linear discriminant analysis is a powerful tool for extracting important features from data. However, a common issue with this method is that the within-class scatter matrix can be singular, making it difficult to find the best features. To address this, an optimal kernel Fisher discriminant analysis (OKFDA) was developed. By using isomorphic mapping, the researchers created a new algorithm to compute the best discriminant vectors even in singular cases. Testing on a subset of face images showed that OKFDA is effective for face recognition.